{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1 - Risk and return models\n",
    "\n",
    "\n",
    "In this section, we compare how well the different risk models predict an out-of-sample covariance matrix, and how well the different returns models predict out-of-sample returns.\n",
    "\n",
    "## Risk models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1.3.1'"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pypfopt\n",
    "from pypfopt import risk_models, expected_returns, plotting\n",
    "pypfopt.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = pd.read_csv(\"data/stock_prices.csv\", parse_dates=True, index_col=\"date\")\n",
    "past_df, future_df = df.iloc[:-250], df.iloc[-250:]\n",
    "future_cov = risk_models.sample_cov(future_df)\n",
    "\n",
    "sample_cov = risk_models.sample_cov(past_df)\n",
    "plotting.plot_covariance(sample_cov, plot_correlation=True)\n",
    "plotting.plot_covariance(future_cov, plot_correlation=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that visually, the sample covariance does not capture some of the new features of the covariance matrix, for example the highly correlated group of FAANG stocks. We may be able to improve this by using an exponentially-weighted covariance matrix, which gives more weight to recent data. We can also look at how each model predicts future variance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "future_variance = np.diag(future_cov)\n",
    "mean_abs_errors = []\n",
    "\n",
    "risk_methods = [\n",
    "    \"sample_cov\",\n",
    "    \"semicovariance\",\n",
    "    \"exp_cov\",\n",
    "    \"ledoit_wolf\",\n",
    "    \"ledoit_wolf_constant_variance\",\n",
    "    \"ledoit_wolf_single_factor\",\n",
    "    \"ledoit_wolf_constant_correlation\",\n",
    "    \"oracle_approximating\",\n",
    "]\n",
    "\n",
    "for method in risk_methods:\n",
    "    S = risk_models.risk_matrix(df, method=method)\n",
    "    variance = np.diag(S)\n",
    "    mean_abs_errors.append(np.sum(np.abs(variance - future_variance)) / len(variance))\n",
    "    \n",
    "xrange = range(len(mean_abs_errors))\n",
    "plt.barh(xrange, mean_abs_errors)\n",
    "plt.yticks(xrange, risk_methods)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the exponential covariance matrix is a much better estimator of future variance compared to the other models. Its mean absolute error is 2%, which is actually pretty good. Let's visually compare the exponential cov matrix to the realised future cov matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "exp_cov = risk_models.exp_cov(past_df)\n",
    "plotting.plot_covariance(exp_cov, plot_correlation=True)\n",
    "plotting.plot_covariance(future_cov, plot_correlation=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Returns\n",
    "\n",
    "What about returns? Will the exponentially-weighted returns similarly be the best performer?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "future_rets = expected_returns.mean_historical_return(future_df)\n",
    "mean_abs_errors = []\n",
    "return_methods = [\n",
    "    \"mean_historical_return\",\n",
    "    \"ema_historical_return\",\n",
    "    \"capm_return\",\n",
    "    ]\n",
    "\n",
    "for method in return_methods:\n",
    "    mu = expected_returns.return_model(past_df, method=method)\n",
    "    mean_abs_errors.append(np.sum(np.abs(mu - future_rets)) / len(mu))\n",
    "    \n",
    "xrange = range(len(mean_abs_errors))\n",
    "plt.barh(xrange, mean_abs_errors)\n",
    "plt.yticks(xrange, return_methods)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.2732675295106068, 0.29740354389638507, 0.28701847303235783]\n"
     ]
    }
   ],
   "source": [
    "print(mean_abs_errors)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The exponential moving average is marginally better than the others, but the improvement is almost unnoticeable. We also note that the mean absolute deviations are above 25%, meaning that if your expected annual returns are 10%, on average the realised annual return could be anywhere from a 15% loss to a 35% gain. This is a massive range, and gives some context to the advice in the docs suggesting that you optimize without providing an estimate of returns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots( 1, len(return_methods),sharey=True, figsize=(15,10))\n",
    "\n",
    "for i, method in enumerate(return_methods):\n",
    "    mu = expected_returns.return_model(past_df, method=method)\n",
    "    axs[i].set_title(method)\n",
    "    mu.plot.barh(ax=axs[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The good news is that we see a good degree of agreement (apart from the `ema` method)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "pyportfolioopt",
   "language": "python",
   "name": "pyportfolioopt"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
